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Question:

If the standard deviation of the numbers -1, 0, 1, k is √5 where k > 0, then k is equal to?

4√5/3

2√6

√6

2√10/3

Solution:

S.D=√Σ(x-x̄)²/n

x̄ = Σx/4 = (-1 + 0 + 1 + k)/4 = k/4
Now √5 = √[((-1-k/4)² + (0-k/4)² + (1-k/4)² + (k-k/4)²)/4]
→ 5 × 4 = 2(1+k²/16)² + 5k²/8
→ 20 = 3k²/4
→ k² = 24
→ k = 2√6.